It was a gritty, draining, fearless victory in an absolute must-win. If they bring the same fire in Game 4, the Rockets are returning to California with a series truly on the line.

The real Rockets returned just in time Saturday night, sharpening everything for national TV eyes.

Harden shook off 14-of-32 shooting to sink a critical 3-pointer late in overtime. Clint Capela was a flying highlight reel. Eric Gordon (30 points, seven made 3s) was the best shooter on the court. Mike D’Antoni’s team ultimately outschemed Steve Kerr’s, winning Game 3 126-121 and pulling within 2-1 in these Western Conference semifinals.

“We showed a lot of character, a lot of fight, and we just couldn’t give up,” D’Antoni said.

And when Curry blew a late slam that average high schoolers make? Toyota Center screamed like the NBA Finals were about to begin in downtown Houston.

Cue the floating post-victory confetti.

“It would have been a steal if we had won that game,” Kerr said.

The Rockets endured a deadly fourth quarter from Durant, who finished with a game-high 46 points and almost made it 3-0 Warriors as a one-man video game.

These Rockets could still take this series. Win Game 4 on Monday night. Claim a victory back at Oracle Arena. Finally overcome Golden State and outfight the Warriors.

“You have to have (swagger and intensity),” Harden said. “If you don’t have it, you might as well leave.”

A red-drenched crowd was ready. Flashing bracelets reminded a national TV audience how critical Game 3 was for the local faithful. But the Rockets initially forgot to hit the “Play better defense” button, while Golden State kept running circles around the squad staring at a season-altering must-win.

Harden keyed the change by altering his initial attack. After three-plus off days devoted to endless questions about red eyes and blurred vision, the Rockets’ leader answered the noise by ignoring his standard 3-pointers and aggressively forcing his way toward the rim.

Then intense defense kept leading to instant offense.

Capela beautifully stuffed a flying Andre Iguodala. P.J. Tucker blocked Curry. A 14-6 Rockets run to close the first quarter was capped by a fiery Chris Paul.

The Rockets spent Games 1 and 2 simply trying to stay within sight of the Warriors. In the first quarter Saturday, D’Antoni’s team finally showed the full-court intensity it had sworn was necessary to stay alive in 2019.

“I’m sure they can play better. I think both teams can play better,” Kerr said. “The thing that jumps out to me on tape is how hard both teams are playing. I think everybody is out there competing like crazy.”

Those prescient words were issued before the constant fury of Game 3.

The Rockets squad that turned a 1-5 start into 53 wins and an easy first-round series victory versus Utah? That team reappeared in the first half Saturday, finally challenging Golden State like it was supposed to.

“They got 17 offensive rebounds. That was the reason why they won,” Durant said. “They definitely played with a lot more force. Crashed the glass.”

Gordon kept firing, hitting 20 points before the break. Durant and Curry combined to shoot just 3-of-13 on 3s in the first half. The Rockets had their swagger back and just kept attacking.

“Here’s the adjustment: We need to play with force, and we need to be fundamentally solid and strong,” Rockets associate head coach Jeff Bzdelik said before Game 3. “We didn’t block off (in Games 1 and 2). We didn’t communicate. The adjustment is we’ve just got to play better. We’ve got to play harder, smarter, meaner, tougher, wiser — all that stuff.”

Durant pulled the Warriors within five, draining a 3 and sinking three free throws. But Paul and Harden followed with back-to-back 3s and the Rockets quickly led by 11 again.

The back and forth didn’t stop.

Midseason addition Iman Shumpert hit a big 3. Curry passed off as the shot clock approached zero, finding Draymond Green just in time for a big 3. For all the Rockets’ Game 3 improvements, they led by only seven entering the final quarter. Then it was down to two, after Durant fired off seven super-smooth points. Then it was suddenly 94-93 Warriors, after Durant poured in 10 points in less than 2 minutes.

“Kevin, he is unstoppable, basically,” Kerr said.

Austin Rivers. Klay Thompson. Harden. Durant.

Loose ball. Rebound. Three-pointer.

Missed shot. Instant transition. Another 3.

It was going to end 3-0 or 2-1. The Rockets would either be very much alive or on the verge of death. A quarter gave way to crucial minutes, then defining seconds, then five more crazy minutes.

Who was going to take this one?

Who had enough?

Harden. Tucker. Then the Rockets standing around Rivers near midcourt, surrounding their teammate as celebratory red and white paper slowly drifted into the stands.

“If you’re going to beat them, you have to fight to the last second,” Tucker said.